Vesey's performance at training camp ultimately will determine where he fits among New York's top nine forwards, but it's likely he lands on the left wing with either center Derek Stepan or newcomer Mika Zibanejad, who was acquired in a trade for center Derick Brassard on July 18.
"It's hard to say. I think he's got an ability to score, he can make plays, he's a very talented player," Gorton said. "Where? What number? What line? I wouldn't want to go down that road and say yet, but I think he can come in and play. I think he's going to come in in training camp and do his best to try to fit in as high as he can in our lineup and that's what we're looking for."
The Rangers, who were eliminated by the Penguins in five games in the Eastern Conference First Round, were seventh in the NHL last season in scoring (2.84 goals per game) and 14th on the power play (18.6 percent).
Vesey scored 56 goals over his final 70 games at Harvard, skates well and possesses a solid wrist shot from the slot. His arrival -- and production --- could prove to be more vital if left wing Rick Nash continues to decline and forward Kevin Hayes, who played a role in the Rangers' ability to sign Vesey having grown up with him in Massachusetts, doesn't have a bounce-back season.
Vesey was a third-round pick (No. 66) of the Nashville Predators at the 2012 NHL Draft, and the Predators hoped to sign him after his season at Harvard ended in March, offering Vesey a spot among their top six forwards heading into the Stanley Cup Playoffs.
Nashville traded Vesey's rights to the Buffalo Sabres for a third-round pick in the 2016 draft on June 20. The Sabres had exclusive negotiating rights with Vesey until Tuesday, when he became an unrestricted free agent.
Islanders captain John Tavares, Penguins captain Sidney Crosby and Blackhawks forward Patrick Kane reportedly each pitched Vesey on joining his team.
Considered to be an NHL-ready player, Vesey had 144 points (80 goals, 64 assists) in 128 games in four seasons at Harvard. He also had three assists in nine games to help the United States win the bronze medal at the 2015 IIHF World Championship.